Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#include <assert.h>
using namespace std;
using i64 = long long;

int main()
{
  i64 n;
  cin >> n;
  vector<i64> a(n);
  for (i64 i = 0; i < n; i++)
    cin >> a[i];
  sort(a.begin(), a.end());
  double ans = 0;
  for (i64 i = 0; i < n; i++)
    for (i64 j = i + 1; j < n; j++)
    {
      i64 k = n - 1;
      while (k == i || k == j)
        k--;
      i64 l = k - 1;
      while (l == i || l == j)
        l--;
      ans = max(ans, (double)(a[k] + a[l]) / (a[j] - a[i]));
    }
  cout << fixed << setprecision(6) << ans << endl;
  return 0;
}